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      SUBROUTINE <a name="DPBTRF.1"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>( UPLO, N, KD, AB, LDAB, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   AB( LDAB, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DPBTRF.18"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a> computes the Cholesky factorization of a real symmetric
</span><span class="comment">*</span><span class="comment">  positive definite band matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The factorization has the form
</span><span class="comment">*</span><span class="comment">     A = U**T * U,  if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment">     A = L  * L**T,  if UPLO = 'L',
</span><span class="comment">*</span><span class="comment">  where U is an upper triangular matrix and L is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KD      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment">          or the number of subdiagonals if UPLO = 'L'.  KD &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment">          matrix A, stored in the first KD+1 rows of the array.  The
</span><span class="comment">*</span><span class="comment">          j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment">          as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j&lt;=i&lt;=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment">          Cholesky factorization A = U**T*U or A = L*L**T of the band
</span><span class="comment">*</span><span class="comment">          matrix A, in the same storage format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= KD+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, the leading minor of order i is not
</span><span class="comment">*</span><span class="comment">                positive definite, and the factorization could not be
</span><span class="comment">*</span><span class="comment">                completed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The band storage scheme is illustrated by the following example, when
</span><span class="comment">*</span><span class="comment">  N = 6, KD = 2, and UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  On entry:                       On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
</span><span class="comment">*</span><span class="comment">      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
</span><span class="comment">*</span><span class="comment">     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Similarly, if UPLO = 'L' the format of A is as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  On entry:                       On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
</span><span class="comment">*</span><span class="comment">     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
</span><span class="comment">*</span><span class="comment">     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Array elements marked * are not used by the routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Contributed by
</span><span class="comment">*</span><span class="comment">  Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
      INTEGER            NBMAX, LDWORK
      PARAMETER          ( NBMAX = 32, LDWORK = NBMAX+1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, I2, I3, IB, II, J, JJ, NB
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      DOUBLE PRECISION   WORK( LDWORK, NBMAX )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.103"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      EXTERNAL           <a name="LSAME.104"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.104"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DGEMM, <a name="DPBTF2.107"></a><a href="dpbtf2.f.html#DPBTF2.1">DPBTF2</a>, <a name="DPOTF2.107"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a>, DSYRK, DTRSM, <a name="XERBLA.107"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( ( .NOT.<a name="LSAME.117"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) .AND.
     $    ( .NOT.<a name="LSAME.118"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.128"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPBTRF.128"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine the block size for this environment
</span><span class="comment">*</span><span class="comment">
</span>      NB = <a name="ILAENV.139"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="DPBTRF.139"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>'</span>, UPLO, N, KD, -1, -1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     The block size must not exceed the semi-bandwidth KD, and must not
</span><span class="comment">*</span><span class="comment">     exceed the limit set by the size of the local array WORK.
</span><span class="comment">*</span><span class="comment">
</span>      NB = MIN( NB, NBMAX )
<span class="comment">*</span><span class="comment">
</span>      IF( NB.LE.1 .OR. NB.GT.KD ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use unblocked code
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DPBTF2.150"></a><a href="dpbtf2.f.html#DPBTF2.1">DPBTF2</a>( UPLO, N, KD, AB, LDAB, INFO )
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use blocked code
</span><span class="comment">*</span><span class="comment">
</span>         IF( <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute the Cholesky factorization of a symmetric band
</span><span class="comment">*</span><span class="comment">           matrix, given the upper triangle of the matrix in band
</span><span class="comment">*</span><span class="comment">           storage.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Zero the upper triangle of the work array.
</span><span class="comment">*</span><span class="comment">
</span>            DO 20 J = 1, NB
               DO 10 I = 1, J - 1
                  WORK( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Process the band matrix one diagonal block at a time.
</span><span class="comment">*</span><span class="comment">
</span>            DO 70 I = 1, N, NB
               IB = MIN( NB, N-I+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Factorize the diagonal block
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="DPOTF2.176"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a>( UPLO, IB, AB( KD+1, I ), LDAB-1, II )
               IF( II.NE.0 ) THEN
                  INFO = I + II - 1
                  GO TO 150
               END IF
               IF( I+IB.LE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Update the relevant part of the trailing submatrix.
</span><span class="comment">*</span><span class="comment">                 If A11 denotes the diagonal block which has just been
</span><span class="comment">*</span><span class="comment">                 factorized, then we need to update the remaining
</span><span class="comment">*</span><span class="comment">                 blocks in the diagram:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    A11   A12   A13
</span><span class="comment">*</span><span class="comment">                          A22   A23
</span><span class="comment">*</span><span class="comment">                                A33
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 The numbers of rows and columns in the partitioning
</span><span class="comment">*</span><span class="comment">                 are IB, I2, I3 respectively. The blocks A12, A22 and
</span><span class="comment">*</span><span class="comment">                 A23 are empty if IB = KD. The upper triangle of A13
</span><span class="comment">*</span><span class="comment">                 lies outside the band.
</span><span class="comment">*</span><span class="comment">
</span>                  I2 = MIN( KD-IB, N-I-IB+1 )
                  I3 = MIN( IB, N-I-KD+1 )
<span class="comment">*</span><span class="comment">
</span>                  IF( I2.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A12
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DTRSM( <span class="string">'Left'</span>, <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>,
     $                           <span class="string">'Non-unit'</span>, IB, I2, ONE, AB( KD+1, I ),
     $                           LDAB-1, AB( KD+1-IB, I+IB ), LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A22
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DSYRK( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, I2, IB, -ONE,
     $                           AB( KD+1-IB, I+IB ), LDAB-1, ONE,
     $                           AB( KD+1, I+IB ), LDAB-1 )
                  END IF
<span class="comment">*</span><span class="comment">
</span>                  IF( I3.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Copy the lower triangle of A13 into the work array.
</span><span class="comment">*</span><span class="comment">
</span>                     DO 40 JJ = 1, I3
                        DO 30 II = JJ, IB
                           WORK( II, JJ ) = AB( II-JJ+1, JJ+I+KD-1 )
   30                   CONTINUE
   40                CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A13 (in the work array).
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DTRSM( <span class="string">'Left'</span>, <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>,
     $                           <span class="string">'Non-unit'</span>, IB, I3, ONE, AB( KD+1, I ),
     $                           LDAB-1, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A23
</span><span class="comment">*</span><span class="comment">
</span>                     IF( I2.GT.0 )
     $                  CALL DGEMM( <span class="string">'Transpose'</span>, <span class="string">'No Transpose'</span>, I2, I3,
     $                              IB, -ONE, AB( KD+1-IB, I+IB ),
     $                              LDAB-1, WORK, LDWORK, ONE,
     $                              AB( 1+IB, I+KD ), LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A33
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DSYRK( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, I3, IB, -ONE,
     $                           WORK, LDWORK, ONE, AB( KD+1, I+KD ),
     $                           LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Copy the lower triangle of A13 back into place.
</span><span class="comment">*</span><span class="comment">
</span>                     DO 60 JJ = 1, I3
                        DO 50 II = JJ, IB
                           AB( II-JJ+1, JJ+I+KD-1 ) = WORK( II, JJ )
   50                   CONTINUE
   60                CONTINUE
                  END IF
               END IF
   70       CONTINUE
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute the Cholesky factorization of a symmetric band
</span><span class="comment">*</span><span class="comment">           matrix, given the lower triangle of the matrix in band
</span><span class="comment">*</span><span class="comment">           storage.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Zero the lower triangle of the work array.
</span><span class="comment">*</span><span class="comment">
</span>            DO 90 J = 1, NB
               DO 80 I = J + 1, NB
                  WORK( I, J ) = ZERO
   80          CONTINUE
   90       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Process the band matrix one diagonal block at a time.
</span><span class="comment">*</span><span class="comment">
</span>            DO 140 I = 1, N, NB
               IB = MIN( NB, N-I+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Factorize the diagonal block
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="DPOTF2.276"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a>( UPLO, IB, AB( 1, I ), LDAB-1, II )
               IF( II.NE.0 ) THEN
                  INFO = I + II - 1
                  GO TO 150
               END IF
               IF( I+IB.LE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Update the relevant part of the trailing submatrix.
</span><span class="comment">*</span><span class="comment">                 If A11 denotes the diagonal block which has just been
</span><span class="comment">*</span><span class="comment">                 factorized, then we need to update the remaining
</span><span class="comment">*</span><span class="comment">                 blocks in the diagram:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    A11
</span><span class="comment">*</span><span class="comment">                    A21   A22
</span><span class="comment">*</span><span class="comment">                    A31   A32   A33
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 The numbers of rows and columns in the partitioning
</span><span class="comment">*</span><span class="comment">                 are IB, I2, I3 respectively. The blocks A21, A22 and
</span><span class="comment">*</span><span class="comment">                 A32 are empty if IB = KD. The lower triangle of A31
</span><span class="comment">*</span><span class="comment">                 lies outside the band.
</span><span class="comment">*</span><span class="comment">
</span>                  I2 = MIN( KD-IB, N-I-IB+1 )
                  I3 = MIN( IB, N-I-KD+1 )
<span class="comment">*</span><span class="comment">
</span>                  IF( I2.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A21
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DTRSM( <span class="string">'Right'</span>, <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>,
     $                           <span class="string">'Non-unit'</span>, I2, IB, ONE, AB( 1, I ),
     $                           LDAB-1, AB( 1+IB, I ), LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A22
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DSYRK( <span class="string">'Lower'</span>, <span class="string">'No Transpose'</span>, I2, IB, -ONE,
     $                           AB( 1+IB, I ), LDAB-1, ONE,
     $                           AB( 1, I+IB ), LDAB-1 )
                  END IF
<span class="comment">*</span><span class="comment">
</span>                  IF( I3.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Copy the upper triangle of A31 into the work array.
</span><span class="comment">*</span><span class="comment">
</span>                     DO 110 JJ = 1, IB
                        DO 100 II = 1, MIN( JJ, I3 )
                           WORK( II, JJ ) = AB( KD+1-JJ+II, JJ+I-1 )
  100                   CONTINUE
  110                CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A31 (in the work array).
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DTRSM( <span class="string">'Right'</span>, <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>,
     $                           <span class="string">'Non-unit'</span>, I3, IB, ONE, AB( 1, I ),
     $                           LDAB-1, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A32
</span><span class="comment">*</span><span class="comment">
</span>                     IF( I2.GT.0 )
     $                  CALL DGEMM( <span class="string">'No transpose'</span>, <span class="string">'Transpose'</span>, I3, I2,
     $                              IB, -ONE, WORK, LDWORK,
     $                              AB( 1+IB, I ), LDAB-1, ONE,
     $                              AB( 1+KD-IB, I+IB ), LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Update A33
</span><span class="comment">*</span><span class="comment">
</span>                     CALL DSYRK( <span class="string">'Lower'</span>, <span class="string">'No Transpose'</span>, I3, IB, -ONE,
     $                           WORK, LDWORK, ONE, AB( 1, I+KD ),
     $                           LDAB-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                    Copy the upper triangle of A31 back into place.
</span><span class="comment">*</span><span class="comment">
</span>                     DO 130 JJ = 1, IB
                        DO 120 II = 1, MIN( JJ, I3 )
                           AB( KD+1-JJ+II, JJ+I-1 ) = WORK( II, JJ )
  120                   CONTINUE
  130                CONTINUE
                  END IF
               END IF
  140       CONTINUE
         END IF
      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span>  150 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DPBTRF.362"></a><a href="dpbtrf.f.html#DPBTRF.1">DPBTRF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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